Unfortunately, I do not see how.

As we all know, N_homeless = N_people - N_homes.

Current regulations effectively forbid to build horrible ugly high-rises that can house 50,000 people in each. Currently, it is only profitable to build luxury houses that nobody can afford.

However, the horrible ugly high-rise has the only one advantage: it is cheap, and everyone can afford it. Even a homeless guy that manage to found a crappy -paying job through his heroic effort.

I only see one way to end homelessness: make housing 20x cheaper than it is now. And that would not be possible without cancelling all housing regulations.